Problem: Express your answer as a mixed number simplified to lowest terms. $6\dfrac{1}{3}-1\dfrac{7}{14} = {?}$
Solution: Simplify each fraction. $= {6\dfrac{1}{3}} - {1\dfrac{1}{2}}$ Find a common denominator for the fractions: $= {6\dfrac{2}{6}}-{1\dfrac{3}{6}}$ Convert ${6\dfrac{2}{6}}$ to ${5 + \dfrac{6}{6} + \dfrac{2}{6}}$ So the problem becomes: ${5\dfrac{8}{6}}-{1\dfrac{3}{6}}$ Separate the whole numbers from the fractional parts: $= {5} + {\dfrac{8}{6}} - {1} - {\dfrac{3}{6}}$ Bring the whole numbers together and the fractions together: $= {5} - {1} + {\dfrac{8}{6}} - {\dfrac{3}{6}}$ Subtract the whole numbers: $=4 + {\dfrac{8}{6}} - {\dfrac{3}{6}}$ Subtract the fractions: $= 4+\dfrac{5}{6}$ Combine the whole and fractional parts into a mixed number: $= 4\dfrac{5}{6}$